A caveat concerning singular value decomposition
A caveat concerning singular value decomposition
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关于奇异值分解的警告
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
P. Sardeshmukh
中科院分区：
文献类型：
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作者：
M. Newman;P. Sardeshmukh
对奇异值分解(SYD)技术从观测值的时间序列中恢复两个变量x和y之间的关系的能力进行了评估。结果表明，只有当(I)连接x和y的变换是正交的，或者(Ii)x或y的协方差矩阵是单位矩阵时，奇异值分解才是严格成功的。在一个简单的二维情况下，还研究了当这些条件不满足时该方法的行为。通过对全球上对流层流函数和涡度场的时间序列进行奇异值分解分析，证明了这一警告在气象背景下可能是相关的。虽然这些场通过球面上的二维拉普拉斯算符联系在一起，但由奇异值分解分析得到的奇异图样对并不是这样相关的。这些结果表明，即使对于第一个奇异值分解对，这个问题也是显而易见的，对于后续的奇异值分解对，问题通常会变得更糟。
Abstract An assessment is made of the ability of the singular value decomposition (SYD) technique to recover the relationship between two variables x and y from a time series of their observations. It is shown that SVD is rigorously successful only in the special cases when either (i) the transformation linking x and y is orthogonal or (ii) the covariance matrix of either x or y is the identity matrix. The behavior of the method when theSE conditions are not met is also studied in a simple two-dimensional case. That this caveat can be relevant in a meteorological context is demonstrated by performing an SVD analysis of a time series of global upper-tropospheric streamfunction and vorticity fields. Although these fields are linked by the two-dimensional Laplacian operator on the sphere, it is shown that the pairs of singular patterns resulting from the SVD analysis are not so related. The problem is apparent even for the first SVD pair and generally becomes worse for succeeding pairs These results suggest ...